Operating a heat exchanger

ABSTRACT

Embodiments of the present disclosure are directed towards methods of operating a heat exchanger including transferring heat from the liquid phase change material to a heat transfer fluid through a heat exchanger surface, forming a solid on the heat exchanger surface, wherein the solid is formed from the liquid phase change material, and heating the heat exchanger surface to form a liquid portion from the solid.

FIELD OF DISCLOSURE

Embodiments of the present disclosure are directed towards methods of operating a heat exchanger, more specifically, embodiments are directed towards methods of operating a heat exchanger that include: transferring heat from a liquid phase change material to a heat transfer fluid through a heat exchanger surface; forming a solid on the heat exchanger surface, wherein the solid is formed from the liquid phase change material; and heating the heat exchanger surface to form a liquid portion from the solid.

BACKGROUND

A heat exchanger is an apparatus which transfers heat from one medium to another medium. For instance, heat may be transferred from one fluid to another fluid. The heat may be transferred by conduction through a material that separates the mediums being used. Heat exchangers may be utilized for a number of various applications including air conditioning, power stations, chemical plants, petroleum refineries, natural-gas processing, and sewage treatment facilities, among others.

SUMMARY

The present disclosure provides methods of operating a heat exchanger including transferring heat from a liquid phase change material to a heat transfer fluid through a heat exchanger surface, forming a solid on the heat exchanger surface, wherein the solid is formed from the liquid phase change material, and heating the heat exchanger surface to form a liquid portion from the solid.

The above summary of the present disclosure is not intended to describe each disclosed embodiment or every implementation of the present disclosure. The description that follows more particularly exemplifies illustrative embodiments. In several places throughout the application, guidance is provided through lists of examples, which examples can be used in various combinations. In each instance, the recited list serves only as a representative group and should not be interpreted as an exclusive list.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of an example of a heat exchanger in accordance with one or more embodiments of the present disclosure.

FIG. 2 is a graphical illustration of data associated with an example of operating a heat exchanger in accordance with one or more embodiments of the present disclosure.

DETAILED DESCRIPTION

Methods of operating a heat exchanger are disclosed herein. Methods disclosed herein can include: transferring heat from a liquid phase change material to a heat transfer fluid through a heat exchanger surface; forming a solid on the heat exchanger surface, wherein the solid is formed from the liquid phase change material; and heating the heat exchanger surface to form a liquid portion from the solid, as discussed further herein.

Embodiments of the present disclosure can provide an improved heat power output, e.g., an improved heat flow. For instance, as heat is transferred from a liquid, e.g., molten, phase change material to a heat transfer fluid through a heat exchanger surface, a portion of the liquid phase change material may be cooled such that a solid is formed on the heat exchanger surface. The presence of the solid on the heat exchanger surface can reduce the heat power output of the heat exchanger, as the solid phase change material has lower thermal conductivity relative to a material of the heat exchanger, e.g., a heat exchanger surface; because of the presence of the solid on the heat exchanger surface heat exchange from the liquid phase change material to the heat exchanger surface is reduced. As mentioned, the heat exchanger surface may be heated, e.g., heated electrically, among others, so that a portion of the solid phase change material is re-liquefied. Advantageously, remaining portions of the solid may then be separated from the heat exchanger surface to provide the improved heat power output as the solid phase change material, having the relatively lower thermal conductivity, is no longer reducing heat exchange from the liquid phase change material to the heat transfer fluid via the heat exchanger surface. Providing the improved heat power output may be advantageous for a number of applications, such as power production applications, where a generally consistent heat power output may be desirable.

Previous methods of providing generally consistent heat power output, e.g., for power production applications, have included increasing a heat exchanger surface area to compensate for formation of solids on the heat exchanger surface area. However, both the size considerations and the cost considerations of these increased surface area heat exchangers are prohibitive.

Embodiments of the present disclosure provide that various heat exchangers may be utilized. For instance, shell and tube heat exchangers, plate heat exchangers, or plate and shell heat exchangers, among others, may be utilized.

FIG. 1 is an illustration of an example of a heat exchanger 102 in accordance with one or more embodiments of the present disclosure.

The heat exchanger 102 includes a heat exchanger material 104. The heat exchanger material 104 can separate mediums being utilized with the heat exchanger 102. The heat exchanger material 104 is thermally conductive. Heat may be transferred by conduction through the heat exchanger material 104, e.g., from a first medium to a second medium. Examples of the heat exchanger material 104 include aluminum, aluminum-brass, brass, carbon steel, carbon-moly, chrome-moly steel, copper, cupro-nickel, Inconel, Monel, nickel, stainless steel, titanium, and combinations thereof, among others. The heat exchanger material 104 may be electrically conductive.

The heat exchanger material 104 can have a thickness 106. The thickness 106 may have different values, e.g., for different applications. The thickness may have a value from 0.01 cm to 25.0 cm. All individual values and subranges from 0.01 cm to 25.0 cm are included; for example, the thickness may have a value from a lower limit of 0.01, 0.05, 0.1, or 0.2 cm to an upper limit of 25.0, 22.5, or 20.0 cm. The thickness 106 may have a single particular value throughout the heat exchanger material 104, or the thickness 106 may have a plurality of particular values throughout the heat exchanger material 104. The heat exchange material 104 may include one material or a number of different materials. The heat exchange material 104 may be a single layer or have multiple layers, e.g., layers have same or different materials and/or thicknesses. For embodiments where the heat exchange material 104 includes multiple layers, any single layer may have a thickness of 0.0001 cm or greater, which contributes to the thickness 106. One or more of the multiple layers may help provide increased surface strength, reduce surface abrasion, and/or enhance electrical conductivity, for instance. While one heat exchanger material 104 is illustrated, embodiments are not so limited. For instance, the heat exchanger 102 may include a plurality of heat exchanger materials 104, e.g., corresponding to tubes or plates.

The heat exchanger material 104 includes a first heat exchanger surface 108 and a second heat exchanger surface 110. Embodiments of the present disclosure provide that the first heat exchanger surface 108 and a second heat exchanger surface 110 are separated by the thickness 106.

The heat exchanger 102 includes a first channel material 112 and a second channel material 114. The first channel material 112 and second channel material 114, as well as any additional channel materials, can be various materials, such as a metal, suitable for use with the heat exchanger 102.

The first channel material 112, the first heat exchanger surface 108, and additional first channel materials not illustrated in FIG. 1 can form a first channel 116. The second channel material 114, the second heat exchanger surface 110, and additional second channel materials not illustrated in FIG. 1 can form a second channel 118. The first channel 116 and the second channel 118 can each independently be utilized as fluid conduits and/or fluid reservoirs. Other portions of the heat exchanger 102, not illustrated in FIG. 1, can provide fluids to the first channel 116 and the second channel 118. The first channel 116 and the second channel 118 can each independently have a number of differing volumes, e.g., based upon various heat exchanger applications.

As mentioned, the heat exchanger material 104 can separate mediums, e.g., fluids, being utilized with the heat exchanger 102. The separated mediums can include a phase change material and a heat transfer fluid. Embodiments of the present disclosure provide that heat can be exchanged from a liquid phase change material to a heat transfer fluid via a heat exchanger surface. As used herein, a “phase change material” refers to a material that transitions from a first state, e.g., a liquid state, to a second state, e.g., a solid state, as heat is transferred from the phase change material. As heat is transferred to the phase change material, being in the solid state, the phase change material can transition to the liquid state. The phase change material, e.g., in the liquid state, may be utilized to store thermal energy.

The liquid phase change material may be at a temperature from −50° C. to 600° C. All individual values and subranges from −50° C. to 600° C. are included; for example, the liquid phase change material be from a lower limit of −50° C., −25° C., 0° C., 25° C. 50° C., 75° C., 100° C., 125° C., 150° C., 160° C., or 175° C. to an upper limit of 600° C., 550° C., 500° C., 450° C., 400° C., 385° C., or 375° C.

Examples of phase change materials include, but are not limited to, paraffin, sugar alcohols, polymers, water, organic acids, salts, chlathrate hydrates, and alkali metal hydroxides. Examples of sugar alcohols include, but are not limited to, pentaerythritol, trimethylolethane, erythritol, mannitol, neopentyl glycol, and combinations thereof. Examples of the polymers include, but are not limited to, polyethylene, polypropylene, polyamides, polycarbonates, polyimides, poly(butadiene), poly(isoprene), poly(hydrogenated butadiene), polyetherester elastomers, ethylene/propylene/diene polystyrene, polyvinyl chloride, and combinations thereof. Examples of the organic acids include, but are not limited to, fatty acids or other organic acids, such as capric acid, lauric acid, myristic acid, palmitic acid, and stearic acid and combinations thereof. Examples of the salts include, but are not limited to, aqueous solutions of salts, salt hydrates, mixtures of salt hydrates, inorganic and organic salts and eutectic blends of salts. As used herein, the term “salt” includes salt hydrates, e.g., solid state salts including water molecules. As an example, a salt may include from 1 to 12 water molecules per anion. One or more embodiments provide that the salt includes an anion selected from nitrates, nitrites, carbonates, hydroxides, and combinations thereof. For a number of applications, it may be desirable to utilize a salt hydrate, e.g., for an application where a decrease in melting and/or freezing temperature is desired. Examples of salts, including salt hydrates, that may be utilized include ammonium and alkali and alkali earth metal salts, such as chlorides, chlorates, nitrates, nitrides, sulfides, phosphates, hydroxides, carbonates, fluorides, bromides, acetates, acetamides and perborates of magnesium, sodium, potassium, calcium, lithium, barium, hydrates thereof, and combinations thereof, among others. Further examples of salts, including salt hydrates, that may be utilized potassium nitrate, sodium nitrate, lithium nitrate, sodium chloride, calcium chloride, lithium chlorate, calcium chloride hexahydrate, magnesium chloride hexahydrate, lithium nitrate trihydrate, sodium acetate trihydrate, and combinations thereof, among others.

As used herein “heat transfer fluid” refers to a material that receives heat from the phase change material. The heat transfer fluid can transport heat, e.g., heat received from the phase change material, to another component, such as an electrical producing process, among others. The heat transfer fluid may be a liquid, a gas, or a combination thereof. Examples of heat transfer fluids include air, water, silicone fluids, inhibited glycol-based fluids, mineral oils, among others. Examples of the heat transfer fluid include fluids available under the tradename DOWTHERM™, available from the Dow Chemical Company. One or more embodiments of the present disclosure provide that the heat transfer fluid may be a phase change material. For instance, the heat transfer fluid may be a liquid that phase changes to a gas as heat is received from the phase change material discussed above.

Embodiments of the present disclosure provide that the liquid phase change material is utilized in either the first channel 116 or the second channel 118, while the heat transfer fluid is utilized in the channel not containing the liquid phase change material. As the liquid phase change material and the heat transfer fluid are located on opposite sides of the heat exchanger material 104, heat can be transferred from the liquid phase change material to the heat transfer fluid by conduction through the heat exchanger material 104.

One or more embodiments of the present disclosure provide that the heat transfer fluid may be utilized batch-wise. For example, the heat transfer fluid may be supplied to a channel, e.g., either the first channel 116 or the second channel 118, where it remains for a predetermined duration and/or until the heat transfer fluid reaches a predetermined temperature. The predetermined duration and/or the predetermined temperature may be different for various applications.

One or more embodiments of the present disclosure provide that the liquid phase change material may be utilized batch-wise. For example, the liquid phase change material may be supplied to a channel, e.g., either the first channel 116 or the second channel 118, where it remains for a predetermined duration and/or until the liquid phase change material reaches a predetermined temperature. The predetermined duration and/or the predetermined temperature may be different for various applications.

One or more embodiments of the present disclosure provide that the heat transfer fluid may be utilized continuously, e.g., the heat transfer fluid may flow. Flow of the heat transfer fluid may be counter-current, co-current, or cross-current relative to a flow of the liquid phase change material. One or more embodiments of the present disclosure provide that the liquid phase change material is stagnant relative to a flow of the heat transfer fluid. Additionally, all or a portion of the heat transfer fluid may phase change, e.g., evaporate, as the heat transfer fluid receives heat from the liquid phase change material. Flows of the heat transfer fluid may be different for various applications.

One or more embodiments of the present disclosure provide that the liquid phase change material may be utilized continuously, e.g., the liquid phase change material fluid may flow. Flow of the liquid phase change material may be counter-current, co-current, or cross-current relative to a flow of the heat transfer fluid. One or more embodiments of the present disclosure provide that the heat transfer fluid is stagnant relative to a flow of the liquid phase change material. Flows of the liquid phase change material may be different for various applications.

As heat is transferred from the liquid phase change material to the heat transfer fluid the liquid phase change material can cool, particularly portions of the liquid phase change material located near, e.g., adjacent to, the heat exchanger material 104. As the liquid phase change material cools, the liquid phase change material can transition to a solid phase.

For embodiments where the liquid phase change material is utilized in the first channel 116, a solid formed from the phase change material can form on the first heat exchanger surface 108. For embodiments where the liquid phase change material is utilized in the second channel 118, a solid formed from the phase change material can form on the second heat exchanger surface 110. As mentioned, the presence of the solid on the heat exchanger surface can undesirably reduce the heat power output of the heat exchanger, as the solid phase change material has a lower thermal conductivity relative to the heat exchanger material 104, which may reduce convection between the liquid phase change material and the heat exchanger material 104.

Embodiments of the present disclosure provide heating the heat exchanger surface to form a liquid portion from the solid. Generally, the liquid portions are formed from solid phase change material that is adjacent to the heat exchanger surface. Heating the heat exchanger surface to form a liquid portion from the solid can provide that a boundary layer of liquid is formed between remaining, e.g. non-liquid, solid phase change material and the heat exchanger surface.

One or more embodiments of the present disclosure provide that heating the heat exchanger surface to form a liquid portion from the solid includes applying an electrical current to the heat exchanger surface. For instance, an electrical input can be coupled to the heat exchanger material 104, the heat exchanger surface 108, and/or the heat exchanger surface 110; an electrical circuit may be switched on to provide the electrical current to the heat exchanger material 104, the heat exchanger surface 108, and/or the heat exchanger surface 110. Energy, provided by the electrical current, can heat the heat exchanger material 104, the heat exchanger surface 108, and/or the heat exchanger surface 110. Heat, provided from the electrical current, can be transferred from the heat exchanger surface to the solid phase change material formed on that particular heat exchanger surface. Because the solid is a phase change material, upon sufficient heating a portion of the solid can transition to the liquid phase, i.e. a liquid portion is formed from the solid.

One or more embodiments of the present disclosure provide that heating the heat exchanger surface to form a liquid portion from the solid includes providing a heated fluid to the channel that is opposite the channel having the solid phase change material formed on the heat exchanger surface. For instance, if the solid phase change material is formed on heat exchanger surface 108, the heated fluid may be provided to the channel 118. Similarly, if the solid phase change material is formed on heat exchanger surface 110, the heated fluid may be provided to the channel 116. Energy, provided by the heated fluid, can heat the heat exchanger material 104 and heat exchanger surfaces 108 and 110. Heat, provided from the heated fluid, can be transferred from the heat exchanger surface to the solid phase change material formed on the particular heat exchanger surface. One or more embodiments of the present disclosure provide that the heated fluid may be the heat transfer fluid, where energy is provided to the heated fluid by other than the phase change material. One or more embodiments of the present disclosure provide that the heated fluid is different than the heat transfer fluid. Examples of the heated fluid include air, silicone fluids, inhibited glycol-based fluids, mineral oils, among others.

One or more embodiments of the present disclosure provide that heating the heat exchanger surface to form a liquid portion from the solid includes providing a thermal conduction source to the heat exchanger surface. The thermal conduction source has more thermal energy, e.g., is at a higher temperature, than the heat exchanger material 104 and heat exchanger surfaces 108 and 110. For instance, a thermal conduction source can be coupled to heat exchanger material 104 and the thermal conduction source may be activated, e.g., switched on, to provide thermal energy to heat exchanger material 104 and heat exchanger surfaces 108 and 110. Energy, provided by the thermal conduction source, can heat the heat exchanger material 104 and heat exchanger surfaces 108 and 110. Heat, provided from the thermal conduction source, can be transferred from the heat exchanger surface to the solid phase change material formed on that particular heat exchanger surface. Various thermal conduction sources known in the art may be utilized.

Heating the heat exchanger surface to form a liquid portion from the solid may be performed at predetermined intervals. For instance, heating the heat exchanger surface to form a liquid portion from the solid

One or more embodiments of the present disclosure provide that heating the heat exchanger surface to form a liquid portion from the solid may be performed according to a predetermined cycle. The heat exchanger surface may be heated, as discussed herein, e.g., by providing the electrical current to the heat exchanger material, multiple times with a time interval between heatings from 10 seconds to 48 hours. All individual values and subranges from 10 seconds to 48 hours are included; for example, heat exchanger surface may be heated with a time interval between heatings from a lower limit of 10 seconds, 30 seconds, 1 minute, 15 minutes, 30 minutes, or 60 minutes to an upper limit of 48 hours, 36 hours, 24 hours, or 12 hours. For instance, following a heating cycle, i.e. heating the heat exchanger surface to form a liquid portion from the solid, the heating may be ceased for a time interval. After that time interval, heating the heat exchanger surface to form a liquid portion from the solid may resume.

One or more embodiments of the present disclosure provide that heating the heat exchanger surface to form a liquid portion from the solid may be performed according to a heat power output decrease. For instance, a baseline heat power output may be determined. As an example, the baseline heat power output may be an average of a number of relative maximum heat power outputs, where a relative maximum heat power output occurs when the heat exchanger surface is free from solid phase change material formed thereon. Heating the heat exchanger surface to form a liquid portion from the solid may be performed when a determined heat power output is decreased 1%, 3%, 5%, 10%, 15%, or 25%, for instance, relative to the baseline heat power output. The decreased percentage values may be different for various applications.

Heating the heat exchanger surface to form a liquid portion from the solid may be performed for a duration from 0.1 seconds to 1 hour. All individual values and subranges from 0.1 seconds to 1 hour are included; for example, the heat exchanger surface may be heated from a lower limit of 0.1 seconds, 0.5 seconds, 1 second, 5 seconds, 10 seconds, or 30 seconds to an upper limit of 1 hour, 0.9 hours, 0.8 hours, or 0.7 hours. For instance, following heating the heat exchanger surface to form a liquid portion from the solid being ceased for a time interval, as discussed herein, the heat exchanger surface may be heated for a duration from 1 second to 1 hour to form a liquid portion from the solid. The duration of heating the heat exchanger surface to form a liquid portion from the solid may be different for various applications.

One or more embodiments of the present disclosure provide separating a portion of the solid from the heat exchanger surface. As mentioned, advantageously, portions of the solid may be separated from the heat exchanger surface to provide an improved heat power output.

One or more embodiments of the present disclosure provide separating a portion of the solid from the heat exchanger surface utilizing a gravitational force. For instance, if the gravitational force is directed toward the first channel material 112 and the liquid phase change material is utilized in the first channel 116, then the solid phase change material may form on the first heat exchanger surface 108. As the first heat exchanger surface 108 is heated to form a liquid portion from the solid, the liquid portion intervening between the heat exchanger surface and the remaining solid can decouple, e.g. release, that remaining solid from the heat exchanger surface. Because the intervening liquid portion has decoupled the remaining solid, a portion of the solid may separate from the heat exchanger surface by the gravitational force. In other words, a portion of the solid may fall from the first heat exchanger surface 108 toward the first channel material 112.

When a gravitational force is utilized for separating a portion of the solid from the heat exchanger surface, the heat exchanger surface may have various angles relative to the gravitational force. For example, the heat exchanger surface may have an angle from 00 to 900 relative to the gravitational force. All individual values and subranges from 00 to 900 are included; for example, the heat exchanger surface may have an angle from a lower limit of 0°, 2°, 5°, or 10° to an upper limit of 90°, 85°, 80°, or 70° relative to the gravitational force.

Separating a portion of the solid from the heat exchanger surface utilizing a gravitational force may occur for a duration from 0.01 seconds to 1 hour. All individual values and subranges from 0.01 seconds to 1 hour are included; for example, separating a portion of the solid from the heat exchanger surface utilizing a gravitational force may occur from a lower limit of 0.01 seconds, 0.1 seconds, 1 second, 5 seconds, 10 seconds, or 30 seconds to an upper limit of 1 hour, 0.7 hours, 0.5 hours, 0.4 hours, 0.2 hours, or 0.1 hours.

One or more embodiments of the present disclosure provide that a density of the solid phase change material can be greater than a density of the liquid phase change material. For instance, the density of the solid phase change material can be at least 3% greater, at least 5% greater, at least 7.5% greater, at least 10% greater, at least 12.5% greater, or at least 15% greater than the density of the liquid phase change material. Providing that the density of the solid phase change material is greater than the density of the liquid phase change material may be advantageous when separating a portion of the solid from the heat exchanger surface utilizing a gravitational force, for instance.

One or more embodiments of the present disclosure provide separating a portion of the solid from the heat exchanger surface includes providing a flow of the liquid phase change material. As mentioned, heating the heat exchanger surface to form a liquid portion from the solid, can provide the liquid portion intervening between the heat exchanger surface and the remaining solid, which can decouple that remaining solid from the heat exchanger surface. Because the intervening liquid portion has decoupled the remaining solid, providing a flow of the liquid phase change material can separate a portion of the solid from the heat exchanger surface. While not wishing to be bound to theory, it is believed that frictional forces between the flow of the liquid phase change material and the solid can provide separation, e.g., by application of a force, of a portion of the solid from the heat exchanger surface. The flow of the liquid phase change material may be an increased flow, as compared to preceding flow of the liquid phase change material having a relatively lesser flow rate and/or pressure. Increased flow, e.g., increased flow rates and/or increased pressures, of the liquid phase change material may be different for various applications. One or more embodiments of the present disclosure provide that the increased flow is a pulsed flow. Durations of the pulsed flow, e.g., pulses of flow having an increased flow rate and/or increased pressure, may be different for various applications.

One or more embodiments of the present disclosure provide that separating a portion of the solid from the heat exchanger surface includes providing a pressure difference, e.g. a first pressure and subsequently a second pressure, for the liquid phase change material. For instance, the liquid phase change material may be located in a particular portion of the channel 116, and a valve (not shown in FIG. 1) in a restricting position, may restrict and/or stop flow of the liquid phase change material to provide a first pressure. As discussed herein, heat from the liquid phase change material can be transferred to the heat transfer fluid through the heat exchanger surface, a solid can be formed on the heat exchanger surface, and the heat exchanger surface can be heated to form a liquid portion from the solid. Thereafter, a second pressure, different than the first pressure may be provided, e.g., by opening the valve, relative to the restricting position. The first pressure may be greater than the second pressure. Due to the different pressures, the liquid phase change material may push a portion of the solid from the heat exchanger surface to provide an improved heat power output.

EXAMPLES

In the Examples, various terms and designations for materials are used including, for instance, the following:

Example 1 was performed as follows. For Example 1, a phase change material (LiNO₃) was utilized. Liquid LiNO₃ was maintained at 257° C. in an insulated glass container by a 500 watt electrical heater. A stainless-steel plate (1.4571 stainless-steel; 170 mm×65 mm×1.5 mm) was fully submerged in the liquid LiNO₃ such that a plane including a longitudinal axis of the stainless-steel plate was parallel to a plane formed by the surface of the liquid LiNO₃. A heat transfer fluid (air, at a temperature of approximately 20° C.) was flowed through a channel (5 mm×50 mm) in the stainless-steel plate at 30,000 liters/minute for approximately 10 minutes; the channel had an inlet and an outlet, each located at the top of the insulated glass container. Heat flowed from the liquid LiNO₃ to the stainless-steel plate to the heat transfer fluid, and visual inspection indicated that a solid material formed on the stainless-steel plate. Thereafter, hot air, at a temperature of approximately 450° C., was flowed through the channel in the stainless-steel plate at 40 liters/minute for approximately 30 minutes; heat from this hot air was transferred to the stainless-steel plate and then to the solid material formed on the stainless-steel plate. Visual inspection indicated that the solid material separated from the stainless-steel plate via a gravitational force and collected in the bottom of the insulated glass container.

Example 2, having Trials 1-3, was performed as follows. For Example 2, a phase change material (LiNO₃) was utilized. At 257° C. liquid LiNO₃ had a density of 1.78 g/cm³, and solid LiNO₃ had a density of 2.16 g/cm³. Liquid LiNO₃ was maintained at 257° C. in an insulated glass container by a 500 watt electrical heater. A dual channel apparatus was utilized. The dual channel apparatus included: a first and a second stainless-steel plate (each plate was 1.4571 stainless-steel; 170 mm×65 mm×1.5 mm); and a block (1.4571 stainless-steel of 152 mm×65 mm×11.5 mm) located between the first and a second stainless-steel plates. The first stainless-steel plate was separated (5 mm) from the block to form a first channel, and the second stainless-steel plate was separated (5 mm) from the block to form a second channel. Each channel was connected to an inlet and an outlet, both located at the top of the insulated glass container. The dual channel apparatus included an upper facing and a lower facing (each facing was 1.4571 stainless-steel) to seal the first and second channels; the upper and lower facings were separated from the first and second stainless-steel plates by ceramic gaskets to thermally and electrically isolate the facings from the plates. The dual channel apparatus was fully submerged in the liquid LiNO₃ such that a plane including a longitudinal axis of the first stainless-steel plate and a plane including a longitudinal axis of the second stainless-steel plate were perpendicular to a plane formed by the surface of the liquid LiNO₃. A heat transfer fluid (air, at a temperature of approximately 340° C.) was flowed at 40 liters/minute to the heat apparatus to account for the heat losses at the top of the apparatus and maintain the energy balance. This was performed due to the apparatus components, such as piping and cables that exit the top of the apparatus and could not be insulated enough in order not to impact the Trials. Before the Trials began, the heat transfer fluid was reduced to a temperature of 90° C. and was flowed through each of the channels for approximately 12 minutes, which cooled the apparatus inlet pipe down to approximately 90° C. (measured via a temperature indication at the inlet of the channels to the plates). Heat flowed from the liquid LiNO₃ respectively to the first and the second stainless-steel plates to the heat transfer fluid; visual inspection indicated that a solid material formed on respective portions of the first and the second submerged stainless-steel plates.

A battery, which was able to supply approximately 2 volts, was coupled to the first stainless-steel plate by an electrical circuitry including two plate connectors (each plate connector was 1.4571 stainless-steel) respectively attached near longitudinally opposite ends of the plate.

Prior to the Trials the electrical circuit was switched on for approximately 102 seconds to heat the first stainless-steel plate and the solid material formed on the plate. Visual inspection indicated that the solid material separated from the first stainless-steel plate and collected in the bottom of the insulated glass container. The electrical circuit was switched off. The second stainless-steel plate was not heated by the electrical circuit and the solid material that was formed on the second stainless-steel plate remained on the plate.

For Trial 1: The electrical circuit was switched on for approximately 149 seconds, following a time interval of approximately 271 seconds from the previous heating of the plate, to heat the first stainless-steel plate and the solid material formed on the plate. Visual inspection indicated that the solid material separated from the first stainless-steel plate and collected in the bottom of the insulated glass container. The electrical circuit was switched off. The second stainless-steel plate was not heated by the electrical circuit and the solid material that was formed on the second stainless-steel plate remained on the plate

For Trial 2: a solid material was again formed on the first stainless-steel plate by the procedure described above. Thereafter, the electrical circuit was again switched on for approximately 175 seconds to heat the first stainless-steel plate and the solid material formed on the plate. Visual inspection indicated that the solid material separated from the first stainless-steel plate and collected in the bottom of the insulated glass container. The electrical circuit was switched off.

For Trial 3: a solid material was again formed on the first stainless-steel plate by the procedure described above. Thereafter, the electrical circuit was again switched on for approximately 167 seconds to heat the first stainless-steel plate and the solid material formed on the plate. Visual inspection indicated that the solid material separated from the first stainless-steel plate and collected in the bottom of the insulated glass container. The electrical circuit was switched off.

For Trials 1-3, heat distribution was determined utilizing the following Formulas:

Q _(a)=∫_(t) ₀ ^(t) ¹ [{dot over (V)} _(air)·ρ_(air) ·cp _(air)·(ϑ_(air out,t) _(x) −ϑ_(air in t) _(x) )]dt  Formula 1:

Q _(b+c)=∫_(t) ₁ ^(t) ³ [{dot over (V)} _(air)·ρ_(air) ·cp _(air)·(ϑ_(air out,t) _(x) −ϑ_(air in t) _(x) )]dt  Formula 2:

Q _(el)=∫_(t) ₀ ^(t) ¹ [_(P) x]dt  Formula 3:

Q _(f)=∫_(t) ₀ ^(t) ¹ [{dot over (V)} _(air)·ρ_(air) ·cp _(air)·[(ϑ_(air out,t) ₀ −ϑ_(air in t) ₀ )−(ϑ_(air out,t) _(x) −ϑ_(air in t) _(x) )]]dt  Formula 4:

Q _(c)=∫_(t) ₁ ^(t) ³ [{dot over (V)} _(air)·ρ_(air) ·cp _(air)·[(ϑ_(air out,t) _(x) −ϑ_(air in t) _(x) )−(ϑ_(air out,t) ₁ −ϑ_(air in t) ₁ )]]dt  Formula 5:

Q _(b) =Q _(b+c) −Q _(c)  Formula 6:

Q _(d) =Q _(el) −Q _(b+c)  Formula 7:

Where:

Q_(a)=Energy charged from LiNO₃ to the heat transfer fluid (air) during LiNO₃ discharge; Q_(b)=Energy charged from LiNO₃ to the heat transfer fluid (air) during electrical heat up; Q_(c)=Electrical energy charged to the heat transfer fluid (air); Q_(d)=Electrical energy charged to the LiNO₃; Q_(el)=Electrical energy charged to the system; and Q_(f)=Energy deduction due to LiNO₃ layer during LiNO₃ discharge.

In determining the heat distributions, a Trial, e.g. Trial 1, which may be considered a cycle, is described as a LiNO₃ discharge time t₁−t₀, a detachment of the solid material time t₂−t₁, and a time between detachment of the solid material and an electrical circuit switch off. During the LiNO₃ discharge time, heat energy Q_(a) is transferred from the LiNO₃ material to the heat transfer fluid (air) via the first stainless-steel plate. The starting heat power {dot over (q)}₀ is decreasing to {dot over (q)}₁ over the time t₁−t₀. The heat energy that was not charged to the heat transfer fluid (air) due to the buildup of the solid LiNO₃ material on the first stainless-steel plate is Q_(f). At t₁ the electrical circuit is switched on and electrical energy Q_(el) is charged to the first stainless-steel plate during the time t₃−t₁. The electricity increases the temperature of the first stainless-steel plate surface where LiNO₃ is heated with the energy Q_(d). The electrical energy Q_(el) also heats up the heat transfer fluid (air) with Q_(c). The total energy charged to the heat transfer fluid (air) between t₃ and t₁ is Q_(b)+Q_(c) which means that it comes from both the electrical circuit Q_(c) and from the LiNO₃ in form of Q_(b).

Data from Trials 1-3 is reported in Table 1.

TABLE 1 Unit Trial 1 Trial 2 Trial 3 Electrical circuit on time Time 19:32:45 19:40:00 19:50:00 Operation time from previous detachment t₁ − t₀ sec 271 285 424 Complete solid material detachment time t₂ − t₁ sec 122 52 160 Duration of electrical circuit being on t₃ − t₁ sec 149 175 167 Average air inlet temperature ϑ_(air in) ° C. 91.3 90.0 88.8 Average air outlet temperature ϑ_(air out) ° C. 207.5 207.1 206.3 Energy transferred from previous solid material Q_(a+b+c) Wh 10.9 11.98 15.42 detachment Energy charged from LiNO₃ to the air during Q_(a) Wh 7.0 7.37 10.98 LiNO₃ discharge Energy charged from LiNO₃ to the air during Q_(b) Wh 3.85 4.52 4.35 electrical heat up Electrical energy charged to the air Q_(c) Wh 0.06 0.09 0.10 Electrical energy charged to LiNO₃ Q_(d) Wh 6.55-17.71 7.64-20.71 7.32-19.85 Energy electrical of provided to the system Q_(el) Wh 6.61-17.77 7.7-20.8 7.42-19.94 Energy deduction due to LiNO₃ solid during LiNO₃ Q_(f) Wh 0.17 0.18 0.23 discharge Energy charged to the air from electricity and Q_(b+c) Wh 3.91 4.61 4.44 LiNO₃ during electricity charge time Energy (not transferred due to solid material Q_(b+e) Wh 0.21 0.23 0.23 thickness increase) “Pseudo efficiency” of detachment Q_(d)/Q_(f) Q_(d)/Q_(f) % 1.0-2.6  0.9-2.3  1.1-3.1  Energy electrical until detachment Q_(el, d) Wh 5.38-14.46 2.3-6.2  7.11-19.12 Proportion of electrical energy applied to energy Q_(el)/ % 60.9-163.7 64.6-173.6 48.1-129.3 removed from LiNO₃ Q_(a+b+c)

FIG. 2 is a graphical illustration 250 of data associated with an example of operating a heat exchanger in accordance with one or more embodiments of the present disclosure. FIG. 2 illustrates data associated with Trials 1-3 of Example 2. FIG. 2 includes measured voltages U₂ in volts of the plate connectors over time on the left y axis and the energy transferred to the heat transfer fluid (air) {dot over (q)}_(air) in Watts on the right y axis, i.e. the heat power output.

{dot over (q)}_(air) was determined utilizing the following Formula:

q _({dot over (a)}ιr) =V _(a{dot over (ι)}r)··ρ_(air) ·cp _(air)·(ϑ_(air out)−ϑ_(air in))  Formula 8:

Where:

{dot over (q)}_(air)=heat power charged to the air in (W/s); {dot over (V)}_(air)=air volume flow passed to the first stainless-steel plate (m³/s); ρ_(air)=density of air at 25° C. (kg/m³); cp_(air)=heat capacity of air at (ϑ_(air out)−ϑ_(air in))/2 (J/kgK); ϑ_(air out)=temperature of air at the outlet of the first stainless-steel plate (° C.); and ϑ_(air in)=temperature of air at the inlet of the first stainless-steel plate (° C.).

Voltages (U₂) of the plate connectors was determined as follows. A copper cable (127 mm²) diameter was used to couple components of the dual channel apparatus, e.g., switches, fuses, battery and connectors, with the plate to the electrical circuit. Voltage measurements, during the Trials 1-3, were taken at several points between the copper cable and the plate to measure the voltages (U₂). For the Trials, the plate connectors were to provide that there was no solid phase change material attached to the connectors when the plate was heated. For the Trials, the connectors were partially submerged in the liquid phase change material. As such, heat generated from the current that flowed through the connectors was also partially transferred to the liquid phase change material and therefore to the plate. This heat was included to the heat balance calculation. Additionally, an estimated proportion of the heat from the connectors may also be transferred to the air above the liquid phase change material surface. Prior to the Trials, voltages of the plate, the plate connectors, and the battery were determined at a temperature of approximately 23° C. Electrical resistances of the plate (R_(plate)) and R_(cable) were calculated determined utilizing the following Formulas:

R _(plate)=

(plate length)/((plate width)(plate thickness))  Formula 8:

R _(cable)=0.123 Ohm/km(7 m)=0.924 mOhm  Formula 9:

Where:

=electrical specific resistance of plate metal; determined by

=a*ϑ²+b*ϑ+c, where: a=−4.50822E−07; b=8.18014E−04; c=7.25792E−01.

Current (I) of the electrical circuit was determined utilizing the following Formula:

I=U _(plate) /R _(plate)  Formula 10:

Where:

U_(plate)=voltage at plate during operation of electrical circuit.

Voltage on the total cable (U_(cable)) was determined utilizing the following Formula:

U _(cable) =R _(cable)(I)  Formula 11:

Voltage on the switches and fuses (U_(sw&fu)) utilized for Trials 1-3 was determined utilizing the following Formula:

U _(sw&fu) =U _(battery) −U _(connector) −U _(cable) −U _(plate)  Formula 12:

Where:

U_(connector)=voltage at connector during operation of electrical circuit; and U_(battery)=voltage at battery during operation of electrical circuit.

Resistances on the connector (R connector), switches and fuses (R sw&fu), and total circuit resistance (R total) utilized for Trials 1-3 was determined utilizing the following Formulas:

R _(connector) =U _(connector) /I  Formula 13:

R _(sw&fu) =U _(sw&fu) /I  Formula 14:

R _(total) =R _(cable) +R _(connector) +R _(sw&fu) +R _(plate)  Formula 15:

Current utilized for Trials 1-3 was determined utilizing the following Formula:

I=U _(battery) /R _(total)  Formula 16:

In preparation for the Trials, U₂ was measured every 1-20 seconds. A minimum and a maximum were determined for every data point at every second during the preparation period. It was estimated that the proportion (Voltage [U₁] of connectors at point farthest from plates)/U₂ and (Voltage [U₃] of connectors at points approximately one half the length of the connectors)/U₂ measured at cold conditions is valid for hot conditions. Also, current calculated for the minimum and the maximum were assumed to be constant. Minimum heat power output and maximum heat power output determined utilizing the following Formulas:

P _(,min) =U _(3,cold) /U _(2,cold) *U ₂ *P _(3,min)=0.81*U ₂/0.7490*197 W  Formula 17:

P _(max) =U _(1,cold) /U _(2,cold) *U ₂ *P _(1,max)=1.28*U _(2,)/0.7730*346 W  Formula 18:

In FIG. 2, each “x” indicates a determined heat power output. Trial 1 had a relative maximum heat power output 252, which corresponded to a beginning of a cycle. The relative maximum heat power output 252 occurred when the first stainless-steel plate was essentially free of solid material formed thereon and the electricity was switched off. For Trial 1, as heat was transferred from the liquid LiNO₃ to the heat transfer fluid, a decreasing heat power output region 254 was observed. As illustrated in FIG. 2, decreasing heat power output region 254 was essentially an exponential decrease. The decreasing heat power output region 254 corresponded to formation of the solid material on the first stainless-steel plate. While not wishing to be bound to theory, it is believed that the exponential decrease of heat power output corresponded to an increasing thickness of the solid material on the first stainless-steel plate. As the electrical circuit was switched, as indicated by voltage measurement 256, on and solid material separated from the first stainless-steel plate, corresponding to time 258, and collected in the bottom of the insulated glass container, a desirable and increasing heat power output region 260 was observed.

Trial 2 had a relative maximum heat power output 262, which corresponded to a beginning of a cycle. The relative maximum heat power output 262 occurred when the first stainless-steel plate was essentially free of solid material formed thereon and the electricity was switched off, e.g., a portion of the solid material on the first stainless-steel plate formed in Trial 1 had been heated to form a liquid so that the remaining portion of the solid material separated from the first stainless-steel plate. For Trial 2, as heat was transferred from the liquid LiNO₃ to the heat transfer fluid, a decreasing heat power output region 264 was observed. As illustrated in FIG. 2, decreasing heat power output region 264 was essentially an exponential decrease. The decreasing heat power output region 264 corresponded to formation of the solid material on the first stainless-steel plate. As the electrical circuit was switched on, as indicated by voltage measurement 266, and solid material separated from the first stainless-steel plate, corresponding to time 268, and collected in the bottom of the insulated glass container, a desirable and increasing heat power output region 270 was observed.

Trial 3 had a relative maximum heat power output 272, which corresponded to a beginning of a cycle. The relative maximum heat power output 272 occurred when the first stainless-steel plate was essentially free of solid material formed thereon and the electricity was switched off, e.g., a portion of the solid material on the first stainless-steel plate formed in Trial 2 had been heated to form a liquid so that the remaining portion of the solid material separated from the first stainless-steel plate. For Trial 3, as heat was transferred from the liquid LiNO₃ to the heat transfer fluid, a decreasing heat power output region 274 was observed. As illustrated in FIG. 2, decreasing heat power output region 274 was essentially an exponential decrease. The decreasing heat power output region 274 corresponded to formation of the solid material on the first stainless-steel plate. As the electrical circuit was switched on, as indicated by voltage measurement 276, and solid material separated from the first stainless-steel plate, corresponding to time 278, and collected in the bottom of the insulated glass container, a desirable and increasing heat power output region 280 was observed. 

1. A method of operating a heat exchanger comprising: transferring heat from a liquid phase change material to a heat transfer fluid through a heat exchanger surface; forming a solid on the heat exchanger surface, wherein the solid is formed from the liquid phase change material; and heating the heat exchanger surface to form a liquid portion from the solid.
 2. The method of claim 1, wherein the solid has a density greater than a density of the liquid phase change material.
 3. The method of claim 1, wherein the liquid phase change material is selected from paraffin, sugar alcohols, thermoplastic polymers, organic acids, water, aqueous solutions of salts, chlathrate hydrates, salt hydrates, mixtures of salt hydrates, salts and eutectic blends of salts, and alkali metal hydroxides.
 4. The method of claim 1, wherein the liquid phase change material is a salt.
 5. The method of claim 4, wherein the salt includes an anion selected from nitrates, nitrites, carbonates, hydroxides, and combinations thereof.
 6. The method of claim 1, wherein heating the heat exchanger surface to form the liquid portion from the solid includes applying an electrical current to the heat exchanger surface.
 7. The method of claim 1, wherein forming the solid on the heat exchanger surface includes forming the solid on a first heat exchanger surface; and heating the heat exchanger surface to form the liquid portion from the solid includes heating a second heat exchanger surface to form the liquid portion from the solid.
 8. The method of claim 1, including separating a portion of the solid from the heat exchanger surface.
 9. The method of claim 8, wherein separating the portion of the solid from the heat exchanger surface utilizes a gravitational force.
 10. The method of claim 8, wherein separating the portion of the solid from the heat exchanger surface includes providing a flow of the phase change material.
 11. The method of claim 8, wherein separating the portion of the solid from the heat exchanger surface includes providing a pressure difference for the phase change material. 